Four pendulums \(A, B, C\) and \(D\) are hanged from the same elastic support as shown in the figure. \(A\)…
Four pendulums \(A, B, C\) and \(D\) are hanged from the same elastic support as shown in the figure. \(A\) and \(C\) are of the same length while \(B\) is smaller than \(A, C\) while \(D\) is longer than \(A\). If \(A\) is given displacement, then at steady state
\(D\) will vibrate with max amplitude
\(C\) will vibrate with max amplitude
B will vibrate with max amplitude
All four will oscillate with equal amplitude
Solution
According to given diagram, length of pendulum \(A\) and \(C\) is same. Hence, time period \(\left(T=2 \pi \sqrt{\frac{l}{g}}\right)\) of pendulum \(A\) and \(C\) is also same.
Therefore, they have same frequency of oscillation. Due to this, resonance takes place and the pendulum \(C\) will vibrate with maximum amplitude.
